Addition of fractions:

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Knowing how to get the LCM of the denominator is very important when adding fractions.

In this lesson we are going to look at fractions with the same denominator.

Tomorrow we will add fractions with different denominators.

Prior knowledge learners should have:

• Converting from an improper fraction to a mixed fraction.

An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number). 

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Given the fraction:

The circled numbers are the steps to follow:

1. Divide the denominator into the numerator ( 4 can go into 10 two times)
2. Write the answer as 2 wholes
3. Multiply the whole with the denominator
4. Subtract this answer from the numerator (What is left after 4 goes into 10 two times)
5. Write the answer as a fraction. (Remember that we are busy with quarters, so the denominator stays 4)
6. Simplify your answer if necessary. (Whatever you do at the top, you must do at the bottom too)

Converting from a mixed fraction to an improper fraction.

A mixed fraction is a whole number and a fraction combined into one "mixed" number. Example: 1½ (one and a half) is a mixed fraction. (Also called a Mixed Number) .

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The easier conversion of the two.

Follow the following steps:

1. Multiply the whole with the denominator        (3x6 =18)
2. Add the numerator to the previous answer      (18 + 2 = 20)
3. Write the answer over the denominator given. (The fraction started over 6, so it stays a denominator of 6)

Adding fractions with the same denominator:

When adding fractions, always make sure that your denominators are the same:

In the examples below, the denominators are the same, so learners may add the fractions together.

1.   

• Only numerators are added together.
• NEVER add the denominators, as you are busy with thirds.
• Explain this by asking your learners, if you have half of a pizza and you add another half you get 1 whole and not a quarter.

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2.  

Looking at the two examples above:

The example on the left takes longer but gets to the same answer.  

1. First we convert the mixed fraction into an improper fraction.
2. Add the two fractions together (Remember the denominators stay the same)
3. Calculating the answer, you will see that now, you have an improper fraction.
4. Convert this improper fraction to a mixed fraction again and simplify if possible.

The example on the right is quite shorter and also gets the same answer.

1. Add the two wholes together as well as the fractions.
2. Simplify your answer.

Conclusion:

• When the denominators of the fractions are the same, fractions may be added together.
• Remind your learners not to add the denominators, as the denominator is the part of the fraction you are working with .
• Only numerators are added together.
• Simplify your answer if possible.